5 papers
Quasi-compactness for dominated kernels with application to quasi-stationary distribution theory
Denis Villemonais
We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremu…
Uniform Wasserstein convergence of penalized Markov processes
Nicolas Champagnat, Edouard Strickler, Denis Villemonais
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a uniqu…
Averaging principle for jump processes depending on fast ergodic dynamics
Vincent Kagan, Edouard Strickler, Denis Villemonais
We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component.…
Quasi-stationary distributions in reducible state spaces
Nicolas Champagnat, Denis Villemonais
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with…
A quasi-stationary approach to the long-term asymptotics of the growth-fragmentation equation
Denis Villemonais, Alexander Watson
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the…